The motion of a particle of mass m is described by the relation, y = ut -1 gt2, where u is the initial velocity of the particle. The force acting on the particle is

To find the force acting on the particle, we use Newton's Second Law of Motion, F = ma, where m is mass and a is acceleration.

• Step 1: Find Velocity (v): The velocity is the first derivative of displacement (y) with respect to time (t). Given y = ut - ½gt², differentiating gives:
  v = dy/dt = u - gt.
• Step 2: Find Acceleration (a): The acceleration is the derivative of velocity with respect to time. Differentiating v = u - gt gives:
  a = dv/dt = -g.
• Step 3: Calculate Force (F): Substituting the acceleration into the force formula:
  F = m × (-g) = -mg.

The negative sign indicates that the force of gravity is acting in the downward direction, opposite to the direction of the initial velocity u. Therefore, Option D is the correct representation of the force acting on the particle.